System and method for an engine controller based on inverse dynamics of the engine

ABSTRACT

Systems and methods for controlling a gas turbine engine are provided. The system comprises an interface to a fuel flow metering valve for controlling a fuel flow to the engine in response to a fuel flow command and a controller connected to the interface and configured for outputting the fuel flow command to the fuel flow metering valve in accordance with a required fuel flow. The controller comprises a feedforward controller configured for receiving a requested engine speed, obtaining a steady-state fuel flow for the requested engine speed as a function of the requested engine speed, the steady-state fuel flow, and the relationship between fuel flow and gas generator speed, and determining the required fuel flow to obtain the requested engine speed and the relationship between fuel flow and gas generator speed.

CROSS-REFERENCE TO RELATED APPLICATIONS

The application claims the benefit of U.S. Provisional PatentApplication No. 62/371,019 filed on Aug. 4, 2016, the contents of whichare hereby incorporated by reference.

TECHNICAL FIELD

The disclosure relates generally to the field of gas turbine enginecontrol, and more particularly, to an engine controller with afeedforward controller.

BACKGROUND

Methodologies used for controlling the acceleration of a gas turbineengine shaft include the use of a feedback controller. However, thereare challenges achieving a desired response time while maintaining acertain stability margin when using a feedback controller. To overcomethis issue, a feedforward controller is used in conjunction with thefeedback controller. The feedforward controller can decrease theresponse time without penalizing stability margin. The feedforwardcontroller is typically tuned iteratively in test. This operation isrepeated for an array of operating points covering the gas turbineengine flight envelope. This method, which requires iterative testing ofthe engine, is resource consuming and expensive when the flight envelopeis large.

Improvements in control systems are therefore desirable.

SUMMARY

In accordance with one broad aspect, there is provided a system forcontrolling a gas turbine engine of an aircraft. The system comprises aninterface to a fuel flow metering valve for controlling a fuel flow tothe engine in response to a fuel flow command and a controller connectedto the interface and configured for outputting the fuel flow command tothe fuel flow metering valve in accordance with a required fuel flow.The controller comprises a feedforward controller configured forreceiving a requested engine speed, obtaining a steady-state fuel flowfor the requested engine speed as a function of the requested enginespeed, the steady-state fuel flow, and the relationship between fuelflow and gas generator speed, and determining the required fuel flow toobtain the requested engine speed and the relationship between fuel flowand gas generator speed.

In accordance with another broad aspect, there is provided a method forcontrolling a gas turbine engine. The method comprises receiving arequested engine speed and obtaining a steady-state fuel flow for therequested engine speed and a relationship between fuel flow and gasgenerator speed. The method further comprises determining the requiredfuel flow to obtain the requested engine speed as a function of therequested engine speed, the steady-state fuel flow, and the relationshipbetween fuel flow and gas generator speed and outputting a command to afuel flow metering valve in accordance with the required fuel flow.

In accordance with yet another broad aspect, there is provided anon-transitory computer-readable medium having stored thereon programcode executable by a processor for controlling a gas turbine engine. Theprogram code comprises instructions for receiving a requested enginespeed and obtaining a steady-state fuel flow for the requested enginespeed and a relationship between fuel flow and gas generator speed. Theprogram code further comprises instructions for determining the requiredfuel flow to obtain the requested engine speed as a function of therequested engine speed, the steady-state fuel flow, and the relationshipbetween fuel flow and gas generator speed and outputting a command to afuel flow metering valve in accordance with the required fuel flow.

DESCRIPTION OF THE DRAWINGS

Reference is now made to the accompanying figures in which:

FIG. 1 is a schematic cross-sectional view of a gas turbine engine;

FIG. 2 is a block diagram of an example aircraft system;

FIG. 3 is a schematic diagram of an example controller for an engine;and

FIG. 4 is a schematic diagram of an example feedforward controller foran engine.

FIG. 5 is a flow chart of an example method performed by a controller.

FIG. 6 is a schematic diagram of an example controller.

DETAILED DESCRIPTION

FIG. 1 illustrates a gas turbine engine 10 of a type provided for use insubsonic flight, generally comprising in serial flow communication a fan12 through which ambient air is propelled, a compressor section 14 forpressurizing the air, a combustor 16 in which the compressed air ismixed with fuel and ignited for generating an annular stream of hotcombustion gases, and a turbine section 18 for extracting energy fromthe combustion gases. High pressure rotor(s) 20 of the turbine section18 are drivingly engaged to high pressure rotor(s) 22 of the compressorsection 14 through a high pressure shaft 24. Low pressure rotor(s) 26 ofthe turbine section 18 are drivingly engaged to the fan rotor 12 and toother low pressure rotor(s) (not shown) of the compressor section 14through a low pressure shaft 28 extending within the high pressure shaft24 and rotating independently therefrom. Although illustrated as aturbofan engine, the gas turbine engine 10 may alternatively be anothertype of engine, for example a turboshaft engine, also generallycomprising in serial flow communication a compressor section, acombustor, and a turbine section, and a fan through which ambient air ispropelled. A turboprop engine may also apply.

FIG. 2 illustrates the gas turbine engine 10 of FIG. 1 within anaircraft 200. Engine thrust is controlled by a full authority digitalelectronic control (FADEC) which regulates the speed of the highpressure rotor(s) 20, 22 and low pressure rotor(s) 26 in response to apilot-operated thrust lever, ambient conditions, pilot selection andaircraft discrete inputs. For simplicity, only the main control systemcomponents of the FADEC, namely a controller or an electronic enginecontrol (EEC) 202, a thrust lever 201, and a fuel flow metering valve204, are illustrated. FADEC works by receiving multiple input variablesof the current flight condition including air density, throttle leverposition, engine temperatures, engine pressures, and many otherparameters. The inputs are received by EEC 202 and analyzed multipletimes per second. Engine operating parameters such as fuel flow, statorvane position, bleed valve position, and others may be computed fromthis data and applied as appropriate. The FADEC may be a single channelFADEC or a dual channel architecture.

The fuel flow metering valve or simply metering valve 204 is connectedto the EEC 202 via an interface or connection 203. The fuel flowmetering valve 204 is arranged to control a fuel flow to the engine inresponse to a fuel flow command from the EEC 202. The metering valve 204is under direct control from EEC 202 and enables thrust control, inresponse to variable guide vane position demands and fuel flow demands.The metering valve 204 provides the engine 10 with fuel from a fuelsource 206 at a required pressure and flow to permit control of enginepower. EEC 202 comprises digital logic to energize the metering valve204. Sensor data obtained for a low rotor and/or a high pressure rotorcan provide information about the speed of the engine 10.

EEC 202 is a controller operationally connected to the fuel flowmetering valve 204 via the interface 203 and configured to generate thesignal representing the final fuel flow rate. For example, EEC 202 maycomprise a feedforward controller 208 and a feedback controller 210. EEC202 is configured to control the gas turbine shaft acceleration throughfuel flow regulation. The feedforward controller 208 allows, inconjunction with the feedback controller 210, the tracking of thereference acceleration without the need for iterative gain tuning.

FIG. 3 shows an example implementation inside EEC 202 of a method tocontrol gas turbine engine 10 in accordance with one embodiment. EEC 202includes a feedforward controller 208 and a feedback controller 210. Asignal 215 representing a requested gas generator speed, denoted byNgreq, is input to the feedforward controller 208. In some embodiments,Ngreq 215 is the requested gas generator shaft speed. Signal Ngreq 215may be obtained from a data table or an outer control loop. For example,Ngreq 215 may be the Ng speed requested by the outer control loop toachieve a certain engine power level, or thrust level. Ngreq 215 mayalso be a speed value selected to avoid a given engine limitation.Feedforward controller 208 is configured to determine and output afeedforward fuel flow WF_(FF) 217. The feedforward fuel flow WF_(FF) 217is used to compute a total fuel flow WF_(tot) and generate a fuel flowsignal Nc 219. The fuel flow signal Nc 219 is then sent to the gasturbine engine 10, represented by plant model 220, as an actuatorcommand for controlling gas turbine speed and acceleration.

In some embodiments, in order to limit engine acceleration to a certainthreshold, the controller 202 receives a reference acceleration, such asthe requested acceleration {dot over (N)}greq 222. A rate-limited gasgenerator speed NgreqRL 232 is obtained by applying the requested gasgenerator speed Ngreq 215 to rate-limiter 216 based on the the requestedacceleration {dot over (N)}greq 222. This way, a time derivative of therate-limited gas generator speed NgreqRL 232 does not exceed therequested acceleration {dot over (N)}greq 222, thereby controllingacceleration of the engine 10. The feedforward fuel flow WF_(FF) 217 maythen be determined based on the rate-limited gas generator speed NgreqRL232. In some embodiments, the reference acceleration is obtained from adata table (not shown). The data table may be pre-determined based oncharacteristics of engine 10.

In some embodiments, the rate-limiter 216 is provided as part offeedforward controller 208, such that feedforward controller 208 maytake Ngreq 215 and apply a rate limit accordingly.

In order to generate the fuel flow command Nc 219, a feedback controller210 may also be implemented, together with the feedforward controller208. The feedback controller 210 forms a closed loop, the feedforwardcontroller 208 forms an open-loop. The feedback controller 210 may beany kind of suitable feedback controller such as aproportional—integral—derivative (PID) controller. A feedback fuel flowWF_(FB) 226 may be generated by the feedback controller 210 and sent tosummation junction 218, together with the feedforward fuel flow WF_(FF)217, to obtain WF_(tot), representing the total fuel flow. Total fuelflow WF_(tot) is used to generate the fuel flow command Nc 219.

In some embodiments, the feedback controller 210 takes as input anacceleration error {dot over (N)}g_(err) 224 that is determined as thedifference between the requested acceleration {dot over (N)}g_(req) 222and a filtered acceleration {dot over (N)}g 228. The requestedacceleration {dot over (N)}g_(req) 222 and the filtered acceleration{dot over (N)}g 228 are sent to a subtraction junction 223 to computethe acceleration error {dot over (N)}g_(err) 224. The filteredacceleration {dot over (N)}g_(err) 228 is removed from the requestedacceleration {dot over (N)}g_(req) 222 to result in the accelerationerror {dot over (N)}g_(err) 224.

The filtered acceleration {dot over (N)}g 228 may be obtained by takinga gas generator speed Ng 221 and feeding it through a filteredderivative function 227, which may generate a numerical derivative. Thegas generator speed Ng 221 may be obtained in a number of ways. Forexample, it may be a measured value of the gas turbine shaft speedobtained from gas engine 10. Alternatively, the gas generator speed Ng221 may be an output of a plant model 220. The plant model 220 may beimplemented based on a function representing suitable engine dynamics ofengine 10, such as the transfer function:

$\frac{K}{{\tau \; s} + 1},$

where τ represents an estimated time constant of the plant model and Krepresents an estimated gain of the plant model. For example, allhardware involved in fuel delivery to the engine 10 and its respectiverelationships may be simplified and modelled in the plant model 220. Theplant model 220 may take the fuel flow command Nc 219 as input andgenerate the gas generator speed Ng 221.

In accordance with some embodiments, a model-based feedforwardcontroller 208 is used to control the acceleration of a gas turbineengine 10 based on engine behavior. For example, it may be modelledbased on inverse dynamics of the engine. The model-based feedforwardcontroller 208 may provide a lead time required to compensate for a lagof the engine.

In some embodiments, the engine behavior can be simplified by a linearmodel of the first-order as seen in equation (1) below. That is, thefeedforward controller 208 may be an inverse dynamics feedforwardcontroller based on an inverse relationship between a fuel flow and aspeed of the gas turbine engine. This relationship may be modelled asequation (1) below:

$\begin{matrix}{{{P(s)} = {\frac{\delta \; {{Ng}(s)}}{\delta \; {{Wf}(s)}} = \frac{K}{{\tau \; s} + 1}}},} & (1)\end{matrix}$

where:

Ng(s) represents a gas generator speed of the engine;

Wf(s) represents a fuel flow

τ is an estimated time constant; and

K is an estimated gain.

This relationship represented by equation (1) above may be valid forsmall variations around a given operating point. This operating point istypically a function of corrected gas generator speed Ng and altitude.The feedforward controller 208 designed based on equation (1) above maynot require any additional tuning and testing. In some embodiments, adriving equation of the feedforward filter of the feedforward controller208 may be given by equation (2) below:

$\begin{matrix}{{\frac{\delta \; {{Wf}_{cmd}(s)}}{\delta \; {{Ng}_{req}(s)}} = \frac{{\tau \; s} + 1}{K}},} & (2)\end{matrix}$

where:

Ng_(req) represents the requested gas generator speed; and

Wf_(cmd) represents a commanding fuel flow of the engine.

Reference is now made to FIG. 4, which shows an example feedforwardcontroller 208 in accordance with one embodiment, implemented based onequation (3) above. The rate-limited requested gas generator speedNgreq_(RL) 232 signal is sent to a differentiator 235. Thedifferentiator may be for example a forward Euler derivative or anyother suitable derivative function. The resulting signal S1 ismultiplied at component 236 by an estimated time constant τ and dividedby the estimated gain K to arrive at signal S2, which is used togenerate the feedforward fuel flow WF_(FF) 217. The feedforwardcontroller 208 is thus built based on a simplified inverse dynamicrelationship of a gas generator.

The feedforward controller 208 may further take as input therate-limited requested gas generator acceleration Ngreq_(RL)*233 and thesteady-state fuel flow WF_(SS)*234. In some embodiments, Ngreq_(RL)*233is a previous value of the rate-limited gas generator speedNgreq_(RL 232) acquired during a previous pass. In some embodiments,WF_(SS)*234 represents a steady state fuel flow for Ngreq_(RL)*233.Ngreq_(RL) 232 and Ngreq_(RL)*233 are used to generate a signal S3,which is sent to a subtraction junction 237 where the Ngreq_(RL)*233signal is subtracted from Ngreq_(RL) 232. The resulting signal S3 isthen divided by the plant model estimated gain K at component 238 togenerate signal S4. Signal S4 is summed at the summation junction 239along with signal S2 and WF_(SS)*234 to determine the feedforward fuelflow WF_(FF) 217, which is the output of feedforward controller 208 andis used to determine the fuel flow Nc 219 as described above.

The systems and methods described herein requires a small amount of datato be computed or obtained. For example, in some embodiments, theparameters required are the plant model estimated time constant τ, plantmodel estimated gain K, and steady-state fuel flow WF_(SS)*234 for aplurality of operating points of the engine. These values may be readilyobtained from a data table that is stored either within or outside EEC202. The data table may be pre-determined based on the characteristicsof engine 10. For example, the values τ, K, and WF_(SS)*may bepre-populated and entered into the data table from running softwaresimulations based on the model or other properties of engine 10. In someembodiments, the values of τ, K change as a function of corrected gasgenerator speed Ng and/or altitude.

Accordingly, in some embodiments, EEC 202 is configured to generate afuel flow command in accordance with a required fuel flow. EEC 202 isconnected to an interface to a fuel flow metering valve for controllingthe fuel flow to the engine in response to the fuel flow command. EEC202 is configured to perform a method for controlling a gas turbineengine. An example embodiment of the method is illustrated in FIG. 5.

At step 510, EEC 202 receives a requested gas generator speed of theengine. At step 520, EEC 202 obtains a steady-state fuel flow for therequested engine speed, and the relationship between fuel flow and gasgenerator speed. As indicated above, the relationship may be modeled asa transfer function of equation (2) or the inverse relationship ofequation (1). At step 530, EEC 202 determines the required fuel flow toobtain the requested gas generator speed as a function of the requestedengine speed, the steady-state fuel flow, and the relationship betweenfuel flow and gas generator speed. At step 540, EEC 202 outputs acommand to a fuel flow metering valve 204, the fuel flow metering valve204 arranged to control a fuel flow to the engine 10.

In some embodiments, the method 500 further comprises a step of limitingacceleration of the gas turbine engine 10 by applying a rate limit tothe requested engine speed, for example using rate limiter 230. In someembodiments, the required fuel flow is adjusted based on an accelerationerror, for example using feedback controller 210, where the accelerationerror is determined based on a reference acceleration and an actualengine acceleration determined from an actual gas generator speed.

FIG. 6 shows a schematic representation of the EEC 202, as a combinationof software and hardware components in a computing device 600. Thecomputing device 600 may comprise one or more processing units 602 andone or more computer—readable memories 604 storing machine-readableinstructions 606 executable by the processing unit 602 and configured tocause the processing unit 602 to generate one or more outputs 610 basedon one or more inputs 608. The inputs may comprise one or more signalsrepresentative of the requested gas generator speed, the time constant,the gain, and the steady state fuel flow. The outputs 610 may compriseone or more signals representative of the feedforward fuel flow, thefeedback fuel flow, and the fuel flow command.

Processing unit 602 may comprise any suitable devices configured tocause a series of steps to be performed by computing device 600 so as toimplement a computer-implemented process such that instructions 606,when executed by computing device 600 or other programmable apparatus,may cause the functions/acts specified in method 500 to be executed.Processing unit 602 may comprise, for example, any type ofgeneral-purpose microprocessor or microcontroller, a digital signalprocessing (DSP) processor, an integrated circuit, a field programmablegate array (FPGA), a reconfigurable processor, other suitably programmedor programmable logic circuits, or any combination thereof.

Memory 604 may comprise any suitable known or other machine-readablestorage medium. Memory 704 may comprise non-transitory computer readablestorage medium such as, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing.Memory 604 may include a suitable combination of any type of computermemory that is located either internally or externally to computingdevice 600 such as, for example, random-access memory (RAM), read-onlymemory (ROM), compact disc read-only memory (CDROM), electro-opticalmemory, magneto-optical memory, erasable programmable read-only memory(EPROM), and electrically-erasable programmable read-only memory(EEPROM), Ferroelectric RAM (FRAM) or the like. Memory 604 may compriseany storage means (e.g. devices) suitable for retrievably storingmachine-readable instructions 606 executable by processing unit 602.

Various aspects of the present disclosure may be embodied as systems,devices, methods and/or computer program products. Accordingly, aspectsof the present disclosure may take the form of an entirely hardwareembodiment, an entirely software embodiment (including firmware,resident software, micro-code, etc.) or an embodiment combining softwareand hardware aspects. Furthermore, aspects of the present disclosure maytake the form of a computer program product embodied in one or morenon-transitory computer readable medium(ia) (e.g., memory 604) havingcomputer readable program code (e.g., instructions 606) embodiedthereon. The computer program product may, for example, be executed by acomputer to cause the execution of one or more methods disclosed hereinin entirety or in part.

Computer program code for carrying out operations for aspects of thepresent disclosure in accordance with instructions 606 may be written inany combination of one or more programming languages, including anobject oriented programming language such as Java, Smalltalk, C++ or thelike and conventional procedural programming languages, such as the “C”programming language or other programming languages. Such program codemay be executed entirely or in part by a computer or other dataprocessing device(s). It is understood that, based on the presentdisclosure, one skilled in the relevant arts could readily writecomputer program code for implementing the methods disclosed herein.

The above description is meant to be exemplary only, and one skilled inthe relevant arts will recognize that changes may be made to theembodiments described without departing from the scope of the inventiondisclosed. For example, the blocks and/or operations in the flowchartsand drawings described herein are for purposes of example only. Theremay be many variations to these blocks and/or operations withoutdeparting from the teachings of the present disclosure. For instance,the blocks may be performed in a differing order, or blocks may beadded, deleted, or modified. The structure illustrated is thus providedfor efficiency of teaching the present embodiment. The presentdisclosure may be embodied in other specific forms without departingfrom the subject matter of the claims. Also, one skilled in the relevantarts will appreciate that while the systems, methods and computerreadable mediums disclosed and shown herein may comprise a specificnumber of elements/components, the systems, methods and computerreadable mediums may be modified to include additional or fewer of suchelements/components. The present disclosure is also intended to coverand embrace all suitable changes in technology. Modifications which fallwithin the scope of the present invention will be apparent to thoseskilled in the art, in light of a review of this disclosure, and suchmodifications are intended to fall within the appended claims.

1. A system for controlling a gas turbine engine of an aircraft, thesystem comprising: an interface to a fuel flow metering valve forcontrolling a fuel flow to the engine in response to a fuel flowcommand; and a controller connected to the interface and configured foroutputting the fuel flow command to the fuel flow metering valve inaccordance with a required fuel flow, the controller comprising afeedforward controller configured for: receiving a requested enginespeed; obtaining a steady-state fuel flow for the requested engine speedas a function of the requested engine speed, the steady-state fuel flow,and the relationship between fuel flow and gas generator speed; anddetermining the required fuel flow to obtain the requested engine speedand the relationship between fuel flow and gas generator speed.
 2. Thesystem of claim 1, wherein the controller is further configured to limitacceleration of the gas turbine engine by applying a rate limit to therequested engine speed.
 3. The system of claim 1, wherein the controllercomprises a feedback controller configured to adjust the required fuelflow based on an acceleration error.
 4. The system of claim 3, whereinthe acceleration error is determined based on a requested engineacceleration and an actual engine acceleration determined from an actualgas generator speed.
 5. The system of claim 1, wherein the feedforwardcontroller is configured to obtain the steady state fuel flow for therequested engine speed from a look-up table.
 6. The system of claim 1,wherein determining the required fuel flow comprises applying theequation:${\frac{\delta \; {{Ng}(s)}}{\delta \; {{Wf}(s)}} = \frac{K}{{\tau \; s} + 1}},$where: Ng(s) represents a gas generator speed of the engine at a givenoperating point s; Wf(s) represents a fuel flow of the engine at thegiven operating point; τ is a time constant of a transfer functionbetween the fuel flow and the gas generator speed; and K is a gain ofthe transfer function between the fuel flow and the gas generator speed.7. The system of claim 6, wherein the given operating point is afunction of a corrected gas generator speed and altitude of theaircraft.
 8. The system of claim 1, wherein determining the requiredfuel flow comprises applying the equation:${\frac{\delta \; {{Wf}_{cmd}(s)}}{\delta \; {{Ng}_{req}(s)}} = \frac{{\tau \; s} + 1}{K}},$where: Ng_(req)(s) represents the requested gas generator speed at agiven operating point s; Wf_(cmd) represents an output of thefeedforward controller at the given operating point s for the requestedgas generator speed; τ is a time constant of a transfer function betweenthe fuel flow and the gas generator speed; and K is a gain of thetransfer function between the fuel flow and the gas generator speed. 9.A method for controlling a gas turbine engine, the method comprising:receiving a requested engine speed; obtaining a steady-state fuel flowfor the requested engine speed and a relationship between fuel flow andgas generator speed; determining the required fuel flow to obtain therequested engine speed as a function of the requested engine speed, thesteady-state fuel flow, and the relationship between fuel flow and gasgenerator speed; and outputting a command to a fuel flow metering valvein accordance with the required fuel flow.
 10. The method of claim 9,further comprising limiting acceleration of the gas turbine engine byapplying a rate limit to the requested engine speed.
 11. The method ofclaim 9, further comprising adjusting the required fuel flow based on anacceleration error.
 12. The method of claim 11, wherein the accelerationerror is determined based on a requested engine acceleration and anactual engine acceleration determined from an actual gas generatorspeed.
 13. The method of claim 9, wherein the steady state fuel flow forthe requested engine speed is obtained from a look-up table.
 14. Themethod of claim 9, wherein determining the required fuel flow comprisesapplying the equation:${\frac{\delta \; {{Ng}(s)}}{\delta \; {{Wf}(s)}} = \frac{K}{{\tau \; s} + 1}},$where: Ng(s) represents a gas generator speed of the engine at a givenoperating point s; Wf(s) represents a fuel flow of the engine at thegiven operating point; τ is a time constant of a transfer functionbetween the fuel flow and the gas generator speed; and K is a gain ofthe transfer function between the fuel flow and the gas generator speed.15. The method of claim 14, wherein the given operating point is afunction of a corrected gas generator speed and altitude of theaircraft.
 16. The method of claim 9, wherein determining the requiredfuel flow comprises applying the equation:${\frac{\delta \; {{Wf}_{cmd}(s)}}{\delta \; {{Ng}_{req}(s)}} = \frac{{\tau \; s} + 1}{K}},$where: Ng_(req)(s) represents the requested gas generator speed at agiven operating point s; Wf_(cmd) represents an output of thefeedforward controller at the given operating point s for the requestedgas generator speed; τ is a time constant of a transfer function betweenthe fuel flow and the gas generator speed; and K is a gain of thetransfer function between the fuel flow and the gas generator speed. 17.A non-transitory computer-readable medium having stored thereon programcode executable by a processor for controlling a gas turbine engine, theprogram code comprising instructions for: receiving a requested enginespeed; obtaining a steady-state fuel flow for the requested engine speedand a relationship between fuel flow and gas generator speed;determining the required fuel flow to obtain the requested engine speedas a function of the requested engine speed, the steady-state fuel flow,and the relationship between fuel flow and gas generator speed; andoutputting a command to a fuel flow metering valve in accordance withthe required fuel flow.
 18. The non-transitory computer-readable mediumof claim 17, wherein the program code further comprises instructions forlimiting acceleration of the gas turbine engine by applying a rate limitto the requested engine speed.
 19. The non-transitory computer-readablemedium of claim 17, wherein the program code further comprisesinstructions for adjusting the required fuel flow based on anacceleration error.
 20. The non-transitory computer-readable medium ofclaim 17, wherein determining the required fuel flow comprises applyingthe equation:${\frac{\delta \; {{Wf}_{cmd}(s)}}{\delta \; {{Ng}_{req}(s)}} = \frac{{\tau \; s} + 1}{K}},$where: Ng_(req)(s) represents the requested gas generator speed at agiven operating point s; Wf_(cmd) represents an output of thefeedforward controller at the given operating point s for the requestedgas generator speed; τ is a time constant of a transfer function betweenthe fuel flow and the gas generator speed; and K is a gain of thetransfer function between the fuel flow and the gas generator speed.